A modification of the quartimax computation for factor rotation is described in which a hypothesized factor pattern is given to the machine along with the data. The machine uses the pattern to select the subset of variables to which it will attend when rotating in a given plane, in order to find an orthogonal solution which closely fits the hypothesis. The program also provides a measure of the goodness of this fit. The program can utilize pattern matrices that reflect only partial hypotheses as to the nature of the factors, as well as those that specify highly determined simple structure.

Intercorrelations among tests nonlinearly related to underlying dimensions require more linear factors than content would demand. For the case of two independent underlying content dimensions, a fictitious example is constructed and made to yield a transformation useful for the nonlinear analysis of certain empirical data. That transformation, when applied to a standard factorization (centroid or principal components if certain symmetries obtain) of the appropriate empirical correlations, yields parameters descriptive of plausible nonplanar regression surfaces for tests on the two underlying dimensions. An empirical example is presented and discussed.

The comparative effects of reward and nonreward on learning are considered in connection with a two-alternative learning situation. Conditions are more general in nature than those discussed in an earlier article. In the statistical model proposed, the question of whether reward and nonreward are equivalent in their effects on learning reduces to testing a composite hypothesis on a multivariate probability distribution. An asymptotic test of this hypothesis is described, and its use is illustrated with data from psychological experiments.

A model for signal detectability suggested by Luce is extended to situations in which the observer is uncertain of some important characteristic of the signal, such as frequency. By making a single assumption concerning the observer's covert response behavior, two solutions are obtained corresponding to qualitatively different behavior. Decrements in detectability and in recognition with uncertainty are shown to be particular functions of discriminability and detectability of the stimuli in other situations. Relevant experimental data are considered.

A matching procedure is proposed by which a judge may use the same items in different matches. The K items in one group most likely to include the correct match with each item in the other are selected. Inclusion of the correct match among the K items chosen is defined as a success. The distribution of the number of successes is discussed. Tables are presented showing the number of successes needed for significance for various values of K and of N, the number of items in each group.

Deuel's rotational method for factor analysis is translated from vector algebra to matrix algebra. A computational example is presented using Deuel's nomogram.

An empirical study of test scores shows the variance of the errors of measurement to be significantly associated with true score in each of four groups studied; it also shows the distribution of the errors of measurement to be significantly skewed in three of these four groups. The mathematical rationale underlying the statistical treatment is presented. Standard error formulas are given for making the necessary significance tests.

The problem of measuring the association between two characters, one quantitative and the other qualitative, is discussed. The formula for the large sample standard error of the point biserial correlation coefficient under general conditions is derived. The point multiserial correlation coefficient is introduced and some of its properties are examined. Tests of different hypotheses appropriate to these types of problems are formulated.

A general critical analysis of the median tests proposed by Wilson for certain analysis of variance hypotheses is presented. Specifically, discrepancies between the purported and actual approximate distributions of some of the test statistics are noted. Validity and power of the resulting tests are discussed.

The weakness in the usual application of the Fisher method of combining probabilities is pointed out and a supplementary method is suggested.